Some Questions Concerning Harmonic Measure

  • Christopher J. Bishop
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 42)


The purpose of this note is to discuss some conjectures concerning harmonic measure. We will start by considering harmonic measure on a simply connected plane domain Ω, but eventually we will also consider some multiply connected and higher dimensional domains. Most of these questions are trivial if ∂Ω has tangents a.e. and many are easy if Ω is only a quasicircle. Thus they are really questions about very non-smooth domains.

Key words

Harmonic measure twist points Hausdorff dimension eigenvalues of Laplacian 


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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Christopher J. Bishop
    • 1
  1. 1.Dept. of MathematicsUCLAUSA

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